Starting from the well-known field theory for directed percolation (DP), we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (Model A)...

We revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class. Our earlier theoretical arguments in favor, supported by evidence from numerical simulations [P.K. Mohanty, D. Dhar, Phys. Rev. Lett. 89 (2002) 104303],...

The Bak–Chen–Tang forest fire model [Phys. Lett. A 147 (1990) 297] was proposed as a toy model of turbulent systems, where energy (in the form of trees) is injected uniformly and globally, but is dissipated (burns) locally. We review our previous results on the model [Phys. Rev. E 62 (2000)...

We investigate the critical behavior of a model that mimics the propagation of an epidemic process over a population mediated by a density of diffusive individuals which can infect a static population upon contact. We simulate the above model on finite chains to determine the critical density of...

We investigate an epidemic spreading process by means of a computational simulation on the Apollonian network, which is simultaneously small-world, scale-free, Euclidean, space-filling and matching graphs. An analysis of the critical behavior of the Contact Process (CP) is presented using a...

We consider directed percolation with an absorbing boundary in 1 + 1 and 2 + 1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard directed percolation 1 + 1 dimension. In addition,...

We introduce a model for the Contact Process with relaxing immunization CPRI. In this model, local memory is introduced by a time and space dependence of the contamination probability. The model has two parameters: a typical immunization time τ and a maximum contamination probability a. The...

A new position-space renormalization group approach is investigated for bond directed percolation in two dimensions. The threshold value for the bond occupation probabilities is found to be pc=0.6443. Correlation length exponents on time (parallel) and space (transverse) directions are found to...

A dimer–dimer reaction model of the type A2+B2→2AB is investigated by means of computer simulations. The desorption of B2 dimer with probability P is studied. Here we investigate the critical behaviour. The critical exponents of our model do not fall into the Reggeon field theory or directed...

We consider a version of directed bond percolation on a square lattice whose vertical edges are directed upward with probabilities pv and horizontal edges are directed rightward with probabilities ph and 1 in alternate rows. Let τ(M,N) be the probability that there is a connected directed path...